I. Economic
Industry structures have traditionally been classified into four possible types: perfect competition, monopoly, oligopoly, and monopolistic competition. Perfect competition is a market structure in which many firms produce an identical product. No individual firm can unilaterally raise the price of its product above market price, nor do firms collude to raise prices. Monopoly is a market structure in which only one firm produces the industry's output. The monopolist may unilaterally raise his price above cost without fear that rivals may undercut his price. Perfect competition cannot be improved on, while natural monopolies are normally regulated.
Most real-world markets have elements of monopolistic competition and/or oligopoly. Oligopoly is an industry structure with only a few firms, so collusion is a serious possibility. Monopolistic competition is an industry structure where products are differentiated. This means that each firm's product is slightly different from every other firm's product, so that each firm is a kind of “mini-monopoly.” Monopolistic competition may or may not have elements of collusion. Oligopoly may or may not have elements of product differentiation.
Collusion can be overt, covert, or tacit. Overt collusion occurs when there is open communication and coordination regarding prices and/or output. Covert collusion occurs when there is secret communication and coordination. Tacit collusion occurs when there is no actual communication, but each firm “understands” the mutual interest of all firms in keeping prices high, and acts accordingly. The prosecution of covert collusion requires direct or indirect evidence of a “conspiracy.” The prosecution of tacit collusion requires the prevention of industry practices which tend to facilitate covert or tacit collusion. Needless to say, this allows many opportunities for collusion which are difficult to prosecute. Additionally, normal oligopoly interaction may result in above-competitive pricing even in the absence of any collusion or product differentiation.
Collusion may occur with varying degrees of success. Completely successful collusion means an industry sells at the monopoly price. Partially successful collusion results in an industry price intermediate between the competitive and monopoly levels. One reason collusion may fail is that firms frequently have an incentive to cheat on any collusive agreement or understanding.
Imperfect competition has two effects. One effect is to decrease the net benefit to consumers (also called consumers' surplus) of consuming a particular good, since the price is now higher. The other effect is to increase the profits to producers of the good. For example, there may be a loss of $150 in net benefits to consumers and a $100 gain in profits to producers. Since the $150 loss is partially offset by a $100 gain, only $50 in lost benefits are accounted by economists as a welfare cost to society as a whole. The remaining $100 loss is offset by a $100 gain, so this amount is accounted by economists as an income transfer from consumers to producers. Elimination of the welfare cost would be a definite benefit to society. Elimination of the income transfers is a benefit to society only to the extent that society views income transfers from consumers to producers as undesirable or undeserved.
Several studies have attempted to estimate the welfare cost of imperfect competition. Scherer's review of these studies concluded that the welfare cost for the U.S. “lies somewhere between 0.5 and 2 percent of gross national product, with estimates nearer the lower bound inspiring more confidence than those on the higher side.” (F. M. Scherer, Industrial Market Structure and Economic Performance, 1980, p. 464.) Some estimates lie above or below Scherer's indicated range. Since G.N.P. is now about $4.5 trillion per year, 1% of G.N.P. is about $45 billion per year. These estimates of welfare cost do not take into account any possible increase in production costs due to lax management under imperfect competition, nor do they attempt to place any value on the possible undesirability of income transfers due to excess profits.
The term “firm”, as understood herein, refers to any proprietorship, partnership, corporation, or other entity which operates within a given industry. Where a particular firm operates in more than one industry, “firm” shall refer only to that part or aspect of the firm's operations, including management compensation and profit calculation, which relates to the industry in question. “Industry” may be flexibly defined, both with respect to the types of goods and services provided and the geographic regions within which the goods or services are produced or sold.
II. Mathematical
A number of elements are used to measure firm performance and the competitive nature of an industry. Definitions of these elements are as follows:
P=Price of Output
Q=Quantity of Output
TC=Total Cost
TR=Total Revenue=P*Q
AC=Average Cost=TC/Q
AR=Average Revenue=TR/Q=P
MC=Marginal Cost=TC′(Q)=dTC/dQ
MR=Marginal Revenue=TR′(Q)=dTR/dQ
π=Profit=TR−TC
The goal of a standard firm is to maximize its profit. A function reaches a maximum or minimum only when its derivative equals zero. When profit is maximized, the derivative of the profit function with respect to any variable under the firm's control is therefore zero. In particular: π′(Q)=dπ(Q)/dQ=0.
Since π(Q)=TR(Q)−TC(Q) (definition), therefore π′(Q)=TR′(Q)−TC′(Q) (derivatives), therefore 0=MR(Q)−MC(Q) (substitutions). Hence, MR=MC or marginal revenue equals marginal cost for any firm which maximizes its profit.
A competitive firm may sell as much output as it likes at the market price. Hence, P(Q)=P, where P is the constant market price. For the competitive firm, TR(Q)=P*Q, so MR(Q)=TR′(Q)=P. Since MR=P for the competitive firm, the competitive firm chooses Q such that P=MR=MC. Hence, price equals marginal cost for all firms in a competitive industry.
A noncompetitive or imperfectly competitive firm may not sell as much output as it likes at the market price. Instead, the noncompetitive firm must lower its price if it wishes to sell more output. Hence, P′(Q)<0, meaning price falls when output rises. For the noncompetitive firm, TR(Q)=P(Q)*Q, so MR(Q)=TR′(Q)=P(Q)+P′(Q)*Q. Since P′(Q)<0 and Q>0, this implies P(Q)>MR(Q). Since P>MR for the noncompetitive firm, the noncompetitive firm chooses Q such that P>MR=MC. Hence, price must exceed marginal cost for at least some firms in a noncompetitive industry.
III. Welfare Economics
Imperfect competition results in an inefficient allocation of society's resources. Resources are efficiently allocated when the total benefits of consumption minus the total costs of production are at a maximum. When efficiency occurs the marginal benefit to consumers of consuming an extra unit of a particular good is just equal to the marginal cost of producing an extra unit of that good. The marginal benefit to consumers is simply the price that consumers pay. Hence, efficiency occurs when price equals marginal cost for all goods.
Under perfect competition price equals marginal cost. Under monopoly, oligopoly, and monopolistic competition price exceeds marginal cost. When price exceeds marginal cost, the marginal benefit of extra consumption exceeds the marginal cost of extra production, so that economic welfare can be increased by producing (and consuming) more of that good. Assuming other objectives will not be adversely affected, the goal of any economic reform should be to set prices as closely as possible to marginal costs. Since there is no necessary relationship between average cost and marginal cost, marginal cost pricing may result in some firms earning an economic profit and other firms running an economic loss.
In perfectly competitive industries marginal cost pricing always occurs. Marginal cost may exceed average cost because an industry temporarily has a short supply of capital relative to demand. Because price exceeds average cost (P=MC>AC), the industry earns positive economic profit or an above-normal rate of return on capital. This attracts new capital into the industry until the industry earns zero economic profit or a normal rate of return on capital. Average cost may exceed marginal cost because an industry temporarily has an oversupply of capital relative to demand. Because price falls below average cost (P=MC<AC), the industry earns negative economic profit (economic loss) or a below-normal rate of return on capital. This induces capital to leave the industry until the industry again earns zero economic profit or a normal rate of return on capital. In the long run a competitive industry can be expected to earn zero economic profit or a normal rate of return on capital. An industry structure can remain competitive, however, only if there are no significant economies of scale.
Economies of scale occur when the average costs of production decline as more output is produced (AC′(Q)<O). For example, it is cheaper per car to produce a million cars than to produce only a thousand cars. It can be shown that when AC′(Q)<0 that MC(Q)<AC(Q). If we set P=MC, then P<AC. Marginal cost pricing results in prices below the average cost of production. If economies of scale are a long-run phenomenon for the industry, marginal cost pricing must result in long-run economic loss. Private firms will not accept such losses unless they are being subsidized. Since the efficient allocation of resources requires marginal cost pricing, efficiency also requires subsidies to industries with long-run economies of scale.
IV. Description of the Prior Art
Prior systems for controlling economic collusion have not suggested that relative profit maximizing incentives be systematically used to reduce or eliminate collusion in an industry context.
Bishop (1960) in his article, “Duopoly: Collusion or Warfare?”, suggests that oligopolistic firms might adopt a principle of maximizing relative rather than absolute profits when engaging in “warfare” rather than collusion. This “warfare” situation is alleged to be a naturally occurring state of affairs whenever there is a disagreement among oligopolists regarding how the jointly maximized profits under collusion should be divided up among the colluders. Bishop's principle of relative profit maximization is used only descriptively, not prescriptively. He suggests no practical application of this principle, nor does he describe any method or system for preventing oligopoly collusion. Bishop merely explains the principle of relative profit maximization and describes some of the first-order mathematical equations which derive from this principle. (See pages 940, 946, 950–961.)
Holmstrom (1982) explores the value of using relative performance evaluations (of workers, executives, etc.) to elicit optimal levels of effort from agents whose actual levels of effort cannot be directly observed. Holmstrom finds that relative performance evaluations will be useful only-if the different agents face some common uncertainties in their environment. (See pages 324, 325, 334–338, 339). By using the relative performance measures, one can at least partially separate out the influence of random environmental variables from the actual efforts of agents, and thereby reward the actual efforts of agents more precisely. In the absence of common uncertainties about which the relative performance evaluations are designed to elicit information, Holmstrom sees no use for relative performance evaluations. Holmstrom states: “Thus, inducing competition among agents by tying their rewards to each other's performance has no intrinsic value. Rather, competition is the consequence of the efficient use of information.” Holmstrom, page 325. (See also pages 324, 335).
As an example of relative performance evaluation systems, Holmstrom mentions “the new executive incentive packages, which base rewards on explicit comparisons with firms within the same industry.” (p. 325; see also pp. 335, 337). Holmstrom does not advocate a system for preventing oligopoly collusion by determining executive compensation on the basis of relative performance measures. Holmstrom sees the value of such compensation methods only as a way of evaluating more accurately the productive efforts of firm managers.
Holmstrom states, at page 337, “After stock options lost their tax advantage (and perhaps also because the market had been depressed in general), performance incentive packages [for executives] became popular.” Holmstrom does not state whether these incentive packages specifically involve relative profit comparisons or whether they involve performance criteria other than relative profit comparisons, nor does he provide references.
In his concluding remarks, page 339, Holmstrom states:
There are other factors of the multiagent problem that have not been addressed in this article, but are worth studying. One concerns the possibility of collusion among agents when relative performance evaluations are used. Collusion may imply restrictions on reward structures. In this regard rank-order tournaments, which induce a zero-sum game between the agents, seem to have an advantage over schemes which are not zero-sum.
This brief comment fails to distinguish between cooperation among agents which furthers a principal's interests from cooperation which goes against a principal's interests, since absolute performance evaluations allow agents to cooperate in ways which further the interests of principals. This analysis is also incomplete because it fails to consider the disutility of effort, as opposed to the utility of income. A rank-order tournament is a zero-sum game only with respect to income, since agents might still wish to collude to reduce overall effort levels, while still maintaining overall income levels.
Fershtman and Judd (1987) discuss a basic theoretical framework which allows managers to have objectives other than simply maximizing profits, and assume that managerial objectives very closely follow the incentives provided to them by the methods of their compensation (p. 927). They analyze the possibilities for interaction among oligopolists, and ascertain what incentive structures for managers would be optimal for the profit-seeking owners of firms, rather than what incentive schemes would be best for society. Collusive behavior by owners or managers is not taken seriously, p. 939, and it is assumed behavior of both owners and managers is noncollusive. The analysis does not consider the possibility that a manager's compensation might be based, at least in part, on another firm's profits (pp. 930–31).